Megan Sexton- Student Work #1

The purpose of this learning task is to see the students level of understanding of knowing how to add three numbers together using a specific method/strategy. This activity falls under the common core standard: "2.NBT.5- Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction." This task is designed to elicit student thinking because the student will have to show work on how they solved the answer and why they did it the way they chose. Based off the work shown, the teacher would be able to see what steps the student took in solving the problem. For example, if the student had the three numbers 10, 10, 9, and he/she showed 10 + 10= 20, then 20 + 9= 29, the teacher is able to see that the student started with base 10's, knowing their tens and that adding two tens gives them 20, then the could just count up from 20 to 9 and get 29. 

The task could be approached in a couple of ways. One way of solving this task with the problem on the right of the image is given the numbers 4, 19, and 20, the student could line up the numbers from greatest to least and see that in the ones column they had 0, 9, and 4. So the student could start by adding 0 + 9= 9 and then add 4 more to get 13. The student could then carry the ten over to the tens place above the 2 and drop the 3. The student will then be able to see that he/she carried 1 over so 1 + 2 = 3 then add 1 more and get 4. The answer then comes out to be 43. Another way the student could solve the task would be the student could take all the tens they see and add them together, so the student would take 10 from 19 and 20 from 20 and add the two together and get 30. Then the student would add what is left over (9+4=13) and add that number (13) to 30 and get the answer as 43. 

I anticipate that Lucy's current mathematical knowledge will allow her to solve the problems easily. For the problem on the left with the numbers 10, 10, and 9, I anticipate Lucy to first add the two tens together then add the remaining number. I know that Lucy understands counting by tens and that this comes fairly easy for her so I anticipate the two tens would be added first. For the problem on the left, I anticipate Lucy to add all her ones then add the numbers in the tens column. I anticipate her to have some trouble with adding the ones and not dropping only the ones down, but dropping the whole number down as well, for example: the number came to be 13, I could anticipate her to drop 13 all together and not just the 3. I also could see an error with not carrying the 1 over to the tens and adding that in the problem as well. 

For the problem on the right the steps Lucy took were as follows:

1. Lucy drew three cards with the numbers, 4, 19, and 20. 
2. She wrote the answers going vertical with 4 on top then 19, then 20. Making sure to keep the ones in line and tens in line. 
3. Lucy added 4 plus 9 = 13 and showed it with a little arrow.
4. Lucy then added 9 + 0= 9 and then added 9 and 13 together to get 22.
5. She showed this by then dropping down the 2 with the arrow then carrying two ones above the tens column. 
6. Lucy then added 1+1+1+2= 5 and got the answer 52.
7. BUT, Lucy understood she made a mistake along the way. She redid the problem below.
8. She did steps 1-3 the same but then instead of adding 9+0 she added 9+4=13 then added 0=13. 
9. She dropped the 3 showing with her arrow and carried the 1 above the ten.
10. Lucy then added 1+1+2=4 and dropped it down.
11. FInalizing her answer as 43.

For the problem on the left:

1. Lucy drew the numbers 10, 10, and 9.
2. Lucy wrote going vertical with 10 on top then 10, then 9. Making sure once again to keep the ones and tens in line.
3. Lucy added 0+0=0 then added 0+9=9.
4. She dropped down the 9, including her arrows to show it.
5. Then she added 1+1=2 and dropped the 2 giving the answer 29. 

After reviewing the work Lucy provided with her math problem, it came to my conclusion that Lucy understands this method of adding three numbers together. It shows that Lucy is able to process numbers in the ones place and numbers in the tens place. Her mathematical thinking provides me with the observation that Lucy knows to only drop the ones place if the number is 13, she understood to only drop the 3 not 13. As well, she shows in her thinking to carry the 1 over to the tens place. I have seen in her thinking that she does get confused with this method in adding on the ones side. As she showed above and fixed, she added 4+9=13 and 9+0=9 then added 13+9 together. But, then below she knew she did not do the problem correctly so she went back and was able to correct her mistake by only adding 3 numbers together total in the ones place. My hypothesis for Lucy's current mathematical thinking is that she is at/above grade level with her understanding on adding and subtracting within 100 by using strategies based on place value.

One way to advance the student's mathematical thinking on problems such as these is instead of her drawing her own cards, I will choose the numbers and make it more challenging. For example, I would choose numbers that when added together give a 100s place such as: 20, 37, and 69. That way I could see Lucy's method that she used above and how she used it with this problem of larger numbers. One other way to advance her mathematical thinking is ask her questions during it, such as from above: "ok, so you did 4+9= 13 now what do you do next? Do you add 13+0=13? Ok, so you have the number 13, is there a tens place in this number? If so, what are we supposed to do?" This way I can really tell if Lucy understands what numbers have tens places, ones places, or even 100s places and what you are supposed to do when you have them. One last way is I could ask Lucy to add the numbers using tens only, so she could add like above, 10+20=30, then she could see the numbers she has left is 9 from the 19 and 4. So she adds 9+4=13 then its easier to just add the 30+13 to get 43.